Distributed Systems

Except as otherwise noted, the content of this presentation is licensed under the Creative Commons Attribution 2.5 License. Page 1 Ngywioggazhon Pystemp Auesfnsicutiwf & Moiiunocaiwn Piqtoaoyp

Page 2 Cryptographic Systems Authentication & Communication Protocols

Page 3 cryptography

κρυπός γραφία

hidden writing

A secret manner of writing, … Generally, the art of writing or solving ciphers. — Oxford English Dictionary

Page 4 cryptology

κρυπός λογια

hidden speaking

1967 D. Kahn, Codebreakers p. xvi, Cryptology is the science that embraces cryptography and cryptanalysis, but the term ‘cryptology’ sometimes loosely designates the entire dual field of both rendering signals secure and extracting information from them. — Oxford English Dictionary

Page 5 Cryptography  Security

Cryptography may be a component of a secure system

Adding cryptography may not make a system secure

Page 6 Terms

Plaintext (cleartext), message M

encryption, E(M)

produces ciphertext, C=E(M)

decryption: M=D(C)

Cryptographic algorithm, cipher

Page 7 Terms: types of ciphers

• restricted cipher

• symmetric algorithm

• public key algorithm

Page 8 Restricted cipher

Secret algorithm

• Leaking • Reverse engineering – HD DVD (Dec 2006) and Blu-Ray (Jan 2007) – RC4 – All digital cellular encryption algorithms – DVD and DIVX video compression – Firewire – Enigma cipher machine – Every NATO and Warsaw Pact algorithm during Cold War

Page 9 The key

BTW, the above is a bump key. See http://en.wikipedia.org/wiki/Lock_bumping.Page 10 The key

Source: en.wikipedia.org/wiki/Pin_tumbler_lock

Page 11 The key

Source: en.wikipedia.org/wiki/Pin_tumbler_lock

Page 12 The key

• We understand how it works: – Strengths – Weaknesses

• Based on this understanding, we can assess how much to trust the key & lock.

Source: en.wikipedia.org/wiki/Pin_tumbler_lock

Page 13 Symmetric algorithm

Secret key

C = EK(M )

M = DK(C )

Page 14 Public key algorithm

Public and private keys

C1 = Epublic(M )

M = Dprivate(C1 )

also:

C2 = Eprivate(M )

M = Dpublic(C2 )

Page 15 McCarthy’s puzzle (1958)

The setting: • Two countries are at war • One country sends spies to the other country • To return safely, spies must give the border guards a password

• Spies can be trusted • Guards chat – information given to them may leak

Page 16 McCarthy’s puzzle

Challenge

How can a guard authenticate a person without knowing the password?

Enemies cannot use the guard’s knowledge to introduce their own spies

Page 17 Solution to McCarthy’s puzzle

Michael Rabin, 1958

Use one-way function, B = f (A) – Guards get B … • Enemy cannot compute A – Spies give A, guards compute f(A) • If the result is B, the password is correct.

Example function: Middle squares • Take a 100-digit number (A), and square it • Let B = middle 100 digits of 200-digit result

Page 18 One-way functions

• Easy to compute in one direction • Difficult to compute in the other

Examples: Factoring: pq = N EASY find p,q given N DIFFICULT Discrete Log: ab mod c = N EASY find b given a, c, N DIFFICULT

Page 19 McCarthy’s puzzle example

Example with an 18 digit number A = 289407349786637777 A2 = 83756614110525308948445338203501729110525308948445338 Middle square, B = 110525308948445338

Given A, it is easy to compute B Given B, it is extremely hard to compute A

Page 20 More terms

• one-way function – Rabin, 1958: McCarthy’s problem – middle squares, exponentiation, … • [one-way] hash function – message digest, fingerprint, cryptographic checksum, integrity check • encrypted hash – message authentication code – only possessor of key can validate message

Page 21 More terms

• Stream cipher – Encrypt a message a character at a time

• Block cipher – Encrypt a message a chunk at a time

Page 22 Yet another term

• Digital Signature – Authenticate, not encrypt message – Use pair of keys (private, public) – Owner encrypts message with private key – Sender validates by decrypting with public key – Generally use hash(message).

Page 23 Cryptography: what is it good for?

• Authentication – determine origin of message

• Integrity – verify that message has not been modified

• Nonrepudiation – sender should not be able to falsely deny that a message was sent

• Confidentiality – others cannot read contents of the message

Page 24 Cryptographic toolbox

• Symmetric encryption

• Public key encryption

• One-way hash functions

• Random number generators

Page 25 Classic Cryptosystems

Page 26 Substitution Ciphers

Page 27 Cæsar cipher

Earliest documented military use of cryptography – Julius Caesar c. 60 BC – shift cipher: simple variant of a substitution cipher – each letter replaced by one n positions away modulo alphabet size n = shift value = key

Similar scheme used in India – early Indians also used substitutions based on phonetics similar to pig latin

Last seen as ROT13 on Usenet to keep the reader from seeing offensive messages unwillingly

Page 28 Cæsar cipher

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z A B C D E F G H I J K L M N O P Q R S T U V WX Y Z

Page 29 Cæsar cipher

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T shift alphabet by n (6)

Page 30 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

Page 31 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

Page 32 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

Page 33 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSW

Page 34 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWU

Page 35 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUN

Page 36 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNB

Page 37 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBU

Page 38 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBUM

Page 39 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBUMZ

Page 40 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBUMZF

Page 41 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBUMZFY

Page 42 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBUMZFYU

Page 43 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBMUFZYUM

Page 44 Cæsar cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z U V WX Y Z A B C D E F G H I J K L M N O P Q R S T

GSWUNBMUFZYUM • Convey one piece of information for decryption: shift value

• trivially easy to crack (26 possibilities for a 26 character alphabet)

Page 45 Ancient Hebrew variant (ATBASH)

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z Z Y XW V U T S R Q P O N M L K J I H G F E D C B A

NBXZGSZHUOVZH • c. 600 BC • No information (key) needs to be conveyed!

Page 46 Substitution cipher

MY CAT HAS FLEAS

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z M P S R L Q E A J T N C I F Z WO Y B X G K U D V H

IVSMXAMBQCLMB • General case: arbitrary mapping • both sides must have substitution alphabet

Page 47 Substitution cipher

Easy to decode: – vulnerable to frequency analysis

Moby Dick Shakespeare (1.2M chars) (55.8M chars)

e 12.300% e 11.797% o 7.282% o 8.299% d 4.015% d 3.943% b 1.773% b 1.634% x 0.108% x 0.140%

Page 48 Statistical Analysis

Letter frequencies E: 12% A, H, I, N, O, R, S, T: 6 – 9% D, L: 4% B, C, F, G, M, P, U, W, Y: 1.5 – 2.8% J, K, Q, V, X, Z: < 1% Common digrams: TH, HE, IN, ER, AN, RE, … Common trigrams THE, ING, AND, HER, ERE, …

Page 49 Polyalphabetic ciphers

Designed to thwart frequency analysis techniques – different ciphertext symbols can represent the same plaintext symbol • 1  many relationship between letter and substitute Leon Battista Alberti: 1466: invented key – two disks J – line up predetermined letter on A inner disk with outer disk – plaintext on inner  ciphertext on outer – after n symbols, the disk is rotated to a new alignment encrypt: AJ decrypt: J A

Page 50 Page 51 Vigenère polyalphabetic cipher

• Blaise de Vigenère, court of Henry III of France, 1518 • Use table and key word to encipher a message • repeat keyword over text: (e.g. key=FACE) FA CEF ACE FACEF .... MY CAT HAS FLEAS • encrypt: find intersection: row = keyword letter column = plaintext letter • decrypt: column = keyword letter, search for intersection = ciphertext letter • message is encrypted with as many substitution ciphers as there are letters in the keyword

Page 52 Vigenère polyalphabetic cipher

plaintext letter

A B C D E F G H I J K L M N O P Q R S T A B C D E F G H I J K L M N O P Q R S T B C D E F G H I J K L M N O P Q R S T U C D E F G H I J K L M N O P Q R S T U V D E F G H I J K L M N O P Q R S T U V W keytext E F G H I J K L M N O P Q R S T U V WX letter F G H I J K L M N O P Q R S T U V WX Y

ciphertext letter

Page 53 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS R

A B C D E F G H I J K L M N O P Q R S T U V WX Y Z B C D E F G H I J K L M N O P Q R S T U V WX Y Z A C D E F G H I J K L M N O P Q R S T U V WX Y Z A B D E F G H I J K L M N O P Q R S T U V WX Y Z A B C E F G H I J K L M N O P Q R S T U V WX Y Z A B C D F G H I J K L M N O P Q R S T U V WX Y Z A B C D E G H I J K L M N O P Q R S T U V WX Y Z A B C D E F H I J K L M N O P Q R S T U V WX Y Z A B C D E F G

Page 54 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY

Page 55 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY E

Page 56 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EE

Page 57 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY

Page 58 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY H

Page 59 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HC

Page 60 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW

Page 61 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW K

Page 62 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW KL

Page 63 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW KLG

Page 64 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW KLGE

Page 65 Vigenère polyalphabetic cipher

FA CEF ACE FACEF MY CAT HAS FLEAS RY EEY HCW KLGEX

Page 66 Vigenère polyalphabetic cipher

"The rebels reposed their major trust, however, in the Vigenere, sometimes using it in the form of a brass cipher disc. In theory, it was an excellent choice, for so far as the South knew the cipher was unbreakable. In practice, it proved a dismal failure. For one thing, transmission errors that added or subtracted a letter ... unmeshed the key from the cipher and caused no end of difficulty. Once Major Cunningham of General Kirby-Smith's staff tried for twelve hours to decipher a garbled message; he finally gave up in disgust and galloped around the Union flank to the sender to find out what it said."

http://rz1.razorpoint.com/index.html

Page 67 Transposition Ciphers

Page 68 Transposition ciphers

• Permute letters in plaintext according to rules

• Knowledge of rules will allow message to be decrypted

• Earliest version used by the Spartans in the 5th century BC – staff cipher

Page 69 Transposition ciphers: staff cipher

MYCATHASFLEAS

MHE

M H E

Page 70 Transposition ciphers: staff cipher

MYCATHASFLEAS

MHE YAA

Y A A

Page 71 Transposition ciphers: staff cipher

MYCATHASFLEAS

MHE YAA CSS

C S S

Page 72 Transposition ciphers: staff cipher

MYCATHASFLEAS

MHE YAA CSS AFx

A F Pad out the text. This is a x block cipher versus a stream cipher

Page 73 Transposition ciphers: staff cipher

MYCATHASFLEAS

MHE YAA CSS Afx TLy

T L y

Page 74 Transposition cipher

Table version of staff cipher – enter data horizontally, read it vertically – secrecy is the width of the table

M Y C A T H A S MYCATHASFLEAS F L E A S x y z

Page 75 Transposition cipher

Table version of staff cipher – enter data horizontally, read it vertically – secrecy is the width of the table

M Y C A T H A S MYCATHASFLEAS MTFS F L E A S x y z

Page 76 Transposition cipher

Table version of staff cipher – enter data horizontally, read it vertically – secrecy is the width of the table

M Y C A T H A S MYCATHASFLEAS MTFSYHLx F L E A S x y z

Page 77 Transposition cipher

Table version of staff cipher – enter data horizontally, read it vertically – secrecy is the width of the table

M Y C A T H A S MYCATHASFLEAS MTFSYHLxCAEy F L E A S x y z

Page 78 Transposition cipher

Table version of staff cipher – enter data horizontally, read it vertically – secrecy is the width of the table

M Y C A T H A S MYCATHASFLEAS MTFSYHLxCAEyASAz F L E A S x y z

Page 79 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S F L E A S x y z

Page 80 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S YHLx F L E A S x y z

YHLx

Page 81 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S YHLxASAz F L E A S x y z ASAz

Page 82 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S YHLxASAzMTFS F L E A S x y z

MTFS

Page 83 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S YHLxASAzMTFSCAEy F L E A S x y z CAEy

Page 84 Transposition cipher with key

– permute letters in plaintext according to key – read down columns, sorting by key

Key: 3 1 4 2 M Y C A MYCATHASFLEAS T H A S YHLxASAzMTFSCAEY F L E A S x y z

Page 85 Combined ciphers

• Combine transposition with substitution ciphers – German ADFGVX cipher (WWI)

• can be troublesome to implement – may require a lot of memory – may require that messages be certain lengths

• Difficult with manual cryptography

Page 86 Electro-mechanical cryptographic engines

Page 87 Rotor machines

1920s: mechanical devices used for automating encryption

Rotor machine:

– set of independently rotating cylinders through which electrical pulses flow

– each cylinder has input & output pin for each letter of the alphabet

– implements a version of the Vigenère cipher

– each rotor implements a substitution cipher

– output of each rotor is fed into the next rotor

Page 88 Rotor machines

• Simplest rotor machine: single cylinder